Sound attenuation in acoustically lined circular ducts in the presence of uniform flow and shear flow

Abstract

An investigation is made of the sound attenuation in a lined circular duct with fluid flow. The eigenvalue equation in the presence of uniform flow is derived based on the continuity of the particle displacement and pressure match on both sides of a vortex sheet located an infinitely small distance from the facing sheet of an acoustic lining. The governing wave equation in the presence of shear flow is replaced by a finite difference equation, and the eigenvalue equation is developed by matching the pressure and the radial component of the velocity at the interface between the regions of uniform flow and shear flow. Solutions of the eigenvalue equations are obtained by an iterative numerical procedure for given duct geometry, mean flow Mach number, boundary layer thickness and acoustic impedance. Theoretical prediction of the sound attenuation spectrum is based on an expression for acoustic energy flow in which the effect of the mean flow is taken into account. It is found in the study of modal attenuation that the fundamental mode (which corresponds to a plane wave perpendicular to the axial flow direction in an unlined duct) is not necessarily the least attenuated in lined circular ducts. Effects of Mach number, boundary layer refraction and acoustic impedance on the sound attenuation are presented for a given duct geometry. Theoretically predicted attenuation spectra are compared with experimental (flow duct) results. The present analysis shows that the effect of the boundary layer refraction on the sound attenuation is greater for upstream wave propagation than for downstream wave propagation.